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Research Papers: Gas Turbines: Structures and Dynamics

# Rotating Flow and Heat Transfer in Cylindrical Cavities With Radial Inflow

[+] Author and Article Information
B. G. Vinod Kumar

e-mail: vb00052@surrey.ac.uk

John W. Chew

e-mail: j.chew@surrey.ac.uk

Nicholas J. Hills

e-mail: n.hills@surrey.ac.uk
Thermo-Fluid Systems UTC,
Faculty of Engineering and Physical Sciences,
University of Surrey,
Guildford, GU2 7XH, UK

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Engineering for Gas Turbines and Power. Manuscript received July 24, 2012; final manuscript received August 20, 2012; published online February 21, 2013. Editor: Dilip R. Ballal.

J. Eng. Gas Turbines Power 135(3), 032502 (Feb 21, 2013) (12 pages) Paper No: GTP-12-1298; doi: 10.1115/1.4007826 History: Received July 24, 2012; Revised August 20, 2012

## Abstract

The design and optimization of an efficient internal air system of a gas turbine requires a thorough understanding of the flow and heat transfer in rotating disc cavities. The present study is devoted to the numerical modeling of flow and heat transfer in a cylindrical cavity with radial inflow and a comparison with the available experimental data. The simulations are carried out with axisymmetric and 3-D sector models for various inlet swirl and rotational Reynolds numbers up to 1.2 × 106. The pressure coefficients and Nusselt numbers are compared with the available experimental data and integral method solutions. Two popular eddy viscosity models, the Spalart–Allmaras and the k-$ɛ$, and a Reynolds stress model have been used. For cases with particularly strong vortex behavior the eddy viscosity models show some shortcomings, with the Spalart–Allmaras model giving slightly better results than the k-$ɛ$ model. Use of the Reynolds stress model improved the agreement with measurements for such cases. The integral method results are also found to agree well with the measurements.

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## Figures

Fig. 1

Schematic of deswirled radial inflow in a rotating cavity

Fig. 2

Mesh used for test case S1

Fig. 3

Radial pressure distribution on the left end wall of the vortex chamber for test case S1 (Cw=2800, Reb=93,600). Wall functions: —, enhanced wall treatment: ---, and Wormley's [4] experiments: ○. Note that the vertical axis represents the ratio of the local gauge pressure to the inlet gauge pressure, as presented by Wormley [4].

Fig. 4

Turbulent viscosity contours predicted by four turbulence models in test case S1

Fig. 5

Mesh used for test case S2

Fig. 6

The tangential velocity profile at the axial midplane of the cavity for test case S2 (Reb=22,000, Cw=2360). Results using (a) eddy viscosity models in the Hydra and integral method, and (b) the RSM model in FLUENT.

Fig. 7

(a) Total temperature at the axial mid plane of the cavity, and (b) local Stanton number on the side wall opposite to the outlet vent at (Reb=200,000 and Cw=14,000) for test case S2

Fig. 8

The nondimensionalized tangential velocity profile at the axial midplane of the cavity for test case R1 (Reφ=3.45 × 105,Cw=1300). Results from turbulence models in (a) the Hydra and integral method, and (b) the FLUENT solver.

Fig. 9

3D geometry used for test case R2.1

Fig. 10

Nondimensional pressure distributions on the left hand disc for the test case R2.1 with Reφ=0.61 × 106, c=0.4, and λt=0.072. Results from the SA model: — the k-ɛ model: – – –, and Farthing's [14] experiments: o.

Fig. 11

Nondimensional pressure distributions on the left hand disc for the test case R2.1 with Reφ=0.61 × 106, c=0.0, and λt=0.120. Results from the SA model: —, the k-ɛ model,: – – –, and Farthing's [11,14] experiments: o.

Fig. 12

Variation of Cp,a with respect to Cw in the cavity in test case R2.2 (Reφ=0.61×106)

Fig. 13

Radial velocity contours on the radial-axial plane, midway between two successive nozzle exits in test case R2.2

Fig. 14

Local Nusselt number on the left hand disc for the test case R3 with Reφ=1.2×106, Cw=3500 and c=1.0. The SA model: —, the k-ɛ model: – – –, and Farthing's [14] experiments: o.

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